The analysis of variance (ANOVA) compares three or more means simultaneously. We determine whether the means are significantly different in the population by analyzing the variation in the dependent variable into separate sources. ANOVA takes advantage of the additivity property of variance, and we partition the variation into treatment effect (real differences) and error (differences due to sampling error or individual differences). The ratio of two variances follows the F (named after R. A. Fisher) distribution. Some readers may have difficulty understanding why the analysis of variance components can be used to test hypotheses about means, but on reflection, one should realize that the variances themselves are based on squared deviations from means.
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